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Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes
Accepted Manuscript Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes A. Nikitin, T. Palin-Luc, A. Shanyavskiy PII: DOI: Reference:
S0142-1123(16)30138-4 http://dx.doi.org/10.1016/j.ijfatigue.2016.05.030 JIJF 3979
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 February 2016 24 May 2016 26 May 2016
Please cite this article as: Nikitin, A., Palin-Luc, T., Shanyavskiy, A., Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes, International Journal of Fatigue (2016), doi: http:// dx.doi.org/10.1016/j.ijfatigue.2016.05.030
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1
Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion
2
loading modes
3
A. Nikitin1,2, T. Palin-Luc 3, A. Shanyavskiy 2, 4*
4
1
5
France
6
2
7
Russia
8
3
9
Metiers, Talence, 33405, France
10
4
LEME, University Paris Ouest Nanterre La Defense, 50, rue de Serves, Ville-d'Avray, 92410,
MAI – National Research University, 4, Volokolamskoe Hwy, A-80, GSP-3, Moscow, 125993,
Arts et Metiers Paris Tech, I2M, CNRS, Universite de Bordeaux, Esplanade des Arts et
SCCAFS, Air. Sheremetevo-1, PO Box 54, Moscow reg., Chimkovskiy state, 141426, Russia
11 12
emails : [email protected], [email protected], [email protected]
13 14
Abstract. This paper is focused on the VHCF behavior of aeronautical titanium alloy
15
under tensile and torsion fatigue loading. Tensile tests were carried out with two different stress
16
ratios: R=-1 and R=0.1. Both surface and subsurface crack initiations were observed. In the case
17
of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were
18
found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-
19
zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R=0.1, have
20
shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation
21
mechanism in presence of positive mean stress. Like for the tensile results, surface and
22
subsurface crack initiation were observed under ultrasonic torsion in spite of the maximum shear
23
stress location on the specimen surface. But the real reason for the subsurface crack initiation
24
under torsion was not found.
25
Keywords: Very-high cycle fatigue, titanium alloy, crack initiation, ultrasonic torsion
26
1
1
Introduction. The problem of fatigue in aeronautical application has a long history [1, 2]
2
and for a long time it was assumed (considered) as low (LCF) and high cycle fatigue (HCF)
3
problems. These two domains were deeply studied for different aeronautical materials, such as
4
aluminum, titanium and nickel based alloys [3]. However, in spite of the developed knowledge
5
about the fatigue behavior of aeronautical materials in the LCF and HCF regimes, some
6
‘unexpected’ in-service failures were reported [4, 5, 6] for compressor and turbine. One of the
7
most critical elements of the aircraft in terms of ‘unexpected failure’ is the turbojet engine. The
8
analysis of typical loading spectrum for blades of turbojet engine has shown that the number of
9
loading cycles for such application can reach 10 10 cycles during in service [7]. The regime of
10
fatigue with ultra long fatigue life is known as very high cycle fatigue (VHCF) or Gigacycle
11
fatigue. Convenient experimental methods are purposed to estimate the fatigue strength at much
12
lower fatigue life (about 10 7, maximum 108 cycles) that is 2 -3 orders of magnitude shorter
13
compared to the real life. Consequentially, conclusion of Nicholas [4] about a premature in-
14
service fatigue failure of titanium compressor of military aircraft was the following: ‘unexpected
15
fatigue failure was due to high frequency loading that lead to accumulation about 10 9 loading
16
cycles during in-service’. Moreover, the fatigue behavior of material in VHCF regime is very
17
sensitive to microstructural features of materials that lead to different types of SN-curves [8].
18
Therefore, nowadays it is impossible to determine the parameters of the SN-curve of a material
19
in VHCF regime without experiment.
20
Usually the critical stress-strain state of fatigue on real elements is estimated by using
21
multiaxial criteria. However, there are no ultrasonic testing methods for multi-axial loading. The
22
only solution for developing multiaxial criteria in VHCF regime is using several testing systems
23
for different loading conditions. Bathias has developed numerous of ultrasonic testing machines
24
such as tension-compression, tension-tension, three points bending [9], torsion [10] and some
25
other systems [7, 11]. It has been shown that the crack initiation mechanism under different
26
loading conditions can be different.
2
1
The purpose of this work is to investigate the crack initiation mechanisms in aeronautical
2
VT3-1 titanium alloy under different loading conditions. Tensile tests under different load ratios
3
were performed together with ultrasonic torsion. Fracture surfaces of all the tested specimens
4
were investigated by SEM in order to identify the crack initiation mechanism.
5 Material and experimental procedure
6
Material
7 8
The studied material in the present work is the forged VT3-1 titanium alloy that is
9
commonly used in the aeronautic industry for compressor disks and blades production. All the
10
specimens were machined from a real compressor disk of a D30 turbojet engine used for Tu-154
11
aircraft, figure 1a.
12
The disk has flown about 16,000 hours. The in-service flown disk was submitted to non
13
destructive controls (ultrasonic NDT and alternating current field measurement) in order to
14
estimate possible accumulated in-service fatigue damages. The results of this after service
15
controls did not reveal degradation of the material due to fatigue (no cracks or material defects).
16
The chemical composition of forged titanium alloy respects to the State standards [12], (Table
17
1).
18 19
Table 1. Chemical composition of forged VT3-1 titanium alloy (w, %) Fe
C
Si
Cr
Mo
N
Al
Zr
O
H
0.2 - 0.7
< 0.1
0.15 - 0.4
0.8 - 2
2-3
< 0.05
5.5 - 7
< 0.5
< 0.15
< 0.015
20 21
The microstructure of this forged VT3-1 titanium alloy is shown in figure 2a. One can see
22
by elongated alpha-platelets with typical length of 10 – 15 micrometers and width of 2-3
23
micrometers, figure 2b. Macroscopically the microstructure of this titanium alloy is strongly
24
inhomogeneous with clear alpha-platelets agglomerations of different sizes and shapes, figure 2c.
3
1
Besides local agglomerations the microstructure is also represented by large continuous areas
2
that are filled with thin, similarly orientated alpha-platelets, figure 2d. Such areas were already
3
observed in a forged titanium alloy and reported in the literature as 'macro-zones' [13].
4
The micro-hardness of this titanium alloy is also inhomogeneous that is stated based on
5
measurements along the specimen’s cross-section diameter. The average value of micro-hardness
6
is 364 HV500 with a maximum deviation of 44 HV500. The value of micro-hardness is related
7
to geometry of alpha-platelets at the location of measurement. Where there is an agglomeration
8
of rough alpha-platelets the micro-hardness value is higher compared to the areas with finer
9
platelets (398 HV for rough and 238 HV for fine alpha-platelets).
10
The mechanical properties were studied by using small tensile specimens machined from
11
the disk’s web, figure 1. Blanks for tensile specimen were taken in circumferential direction. Flat
12
tensile specimens had a thickness of 1 mm, a total length of 75 mm, a length of the working
13
section of 25 mm and a working section width of 5 mm. Monotonic tensile tests were carried out
14
with a displacement rate of 0,075 mm/min. Additionally, the dynamic modulus was determined
15
at 20 kHz. All the mechanical properties are given in Table 2.
16 17
Table 2. Mechanical properties of forged VT3-1 titanium alloy Young's modulus,
UTS [MPa]
[GPa] 114
989
Yield
Elongation
Volumetric
Dynamic
stress
at rupture
mass
modulus
[MPa]
[%]
kg.m-3
[GPa]
960
6
4500
116
18 19
Experimental procedures
20
Two types of fatigue tests in VHCF regime (tensile and torsion) were carried out by using
21
ultrasonic fatigue testing systems. Tensile fatigue tests were performed on a LASUR
22
piezoelectric machine [7] under fully reversed (R=-1) and asymmetric (R=0.1) loadings at 20
4
1
kHz up to the specimen failure or run-out limit of 5x109 cycles for the tensile tests and 109 cycles
2
for the torsion one. The torsion fatigue tests were performed on a self-designed piezoelectric
3
torsion system [14] under fully-reversed (R=-1) loading. All the tests were carried out in
4
laboratory air at room temperature (compressed air cooling). The temperature of the specimen
5
surface was measured by infrared camera measurements for some of the tested specimens. To do
6
that, some tensile and torsion specimens were painted in matt black for the tests with surface
7
temperature measurement at different stress levels (from 100 to 400 MPa for tensile tests and
8
240 MPa for torsion). All the tests were performed with air cooling (like under all the fatigue
9
tests) and a base for one test was 5 ⋅ 10 6 cycles. It was pointed out that at each load level the
10
surface temperature gets stable (horizontal line on graph temperature versus time) after a few
11
seconds of the test. The results of these tests have shown that the maximum increase of
12
temperature due to self heating was less than 10 oC [14].
13
Specimens for ultrasonic fatigue tests were machined from different areas of the
14
compressor disk, figure 1b. Tensile fatigue specimens, figure 1c and 1d were machined from
15
both the rim and the web parts of the disk while torsion specimens, figure 1e, were cut from the
16
rim part only. Several sets of tensile fatigue specimens were prepared: (1) specimens for fully-
17
reversed (R=-1) tests were machined from the rim part in axial direction, figure 1b and from web
18
part in radial direction; (2) specimens for asymmetric (R=0.1) tests were machined from web
19
part in radial and circumferential directions, figure 1b. The surface of all the specimens was
20
mechanically polished with emery paper up to grade 1000. Machining and mechanical polishing
21
may introduce a residual stresses that could affect the crack initiation mechanism. These residual
22
stresses could lead to near to surface crack initiation. Such influence of residual stresses was
23
already discussed for the case of ultrasonic torsion tests on steels. It was found that subsurface
24
torsion crack can initiate from the subsurface in the presence of high residual stresses [15]. In the
25
present study the residual stresses were not measured due to limitations of X-ray diffraction
5
1
instrument because of the complex microstructure of this alloy. The uncertainty of the
2
measurements was higher that the measured values.
3 4
Results and discussions Tensile fully-reversed (R=-1) tests
5
The results of the tests are presented in figure 3. As usual with increasing stress
6
amplitude the fatigue life decreases but we can observe very large scatter. In HCF regime fatigue
7
failures were mainly observed under stress amplitudes of 415 – 430 MPa that is about 43% of
8
ultimate tensile strength. However, there is one stand out result that was obtained under lower
9
stress amplitude after a short fatigue life (in HCF region). The fracture surface analysis by SEM
10
for this specimen has shown subsurface crack initiation with quite damaged origination site. It
11
seems that such initiation is related to some sort of microstructural defect that was not yet found
12
on observed micro-sections. The results of the fatigue tests show a large scatter of fatigue life
13
that reach three orders of magnitude under certain stress amplitudes. In spite of so large scatter a
14
trend line built by least square method is straight decreasing line with clear slope of the SN -
15
curve. Thus, we can say that forged VT3-1 does not show a horizontal asymptote like many
16
others structural materials [8] and there is no infinite fatigue life [16, 17]. A similar result has
17
been reported for Ti-6Al-4V titanium alloy by Janecek [18] in VHCF regime under fully-
18
reversed loading (R=-1) at 20 kHz. It has been stated that the SN curves exhibit a continuous
19
decrease of the stress amplitude with increasing number of cycles from 104 to 109 cycles.
20
In our experiments the analysis of the fracture surfaces has shown two principal crack
21
initiation locations: surface and subsurface. This result is common for two-phase titanium alloy
22
and was already reported for different alloy [18, 19]. However, in order to understand the reason
23
of so large scatter of the fatigue life (figure 3), the fracture surface of all the specimens was
24
analyzed by using scanning electron microscope (SEM). From these fractographic analyses it
25
was found that under high stress amplitudes and short fatigue life crack initiation site is observed
26
at the specimen surface. Detailed analysis on crack initiation sites by SEM allows us to outline
6
1
several 'fatigue life controlling' mechanisms. Specimens with shorter fatigue life and subsurface
2
crack initiations have a strong defect of the microstructure at crack initiation site, figure 4a.
3
Strong defects of microstructure produce a quasi-brittle pattern with clear traces of cracked
4
alpha-platelets. The geometry of these quasi-brittle zones and traces of alpha-platelet allow us to
5
associate these defects with an agglomeration of rough alpha-platelets, figure 2c.
6
With increasing the fatigue life there is a quota of specimens with crack initiation from
7
strong defects is decreasing. In this case another crack initiation mechanism starts to dominate
8
over the previous one. In longer fatigue life, fatigue crack is typically initiated from the border of
9
‘macro-zones’ that are large areas formed by similarly orientated alpha-platelets [13], figure 4b.
10
Within such zone all the alpha-platelets have almost the same crystallographic orientation that
11
allows easier dislocation moving on long distance. The border of two 'macro-zones' is an
12
important barrier for dislocation moving that makes the 'macro-zone' border a stock of the large
13
number of dislocations. Micro-plasticity accumulated at 'macro-zones' borders lead to crack
14
initiation.
15
The specimens failed after longest fatigue lives are typically showing two similar crack
16
initiation sites: quasi-smooth and smooth facets, figure 4c and 4d respectively. These facets are
17
formed due to failure of alpha-platelets or alpha-grains [20, 21]. Figure 4 c and d illustrate a 3D
18
model of individual alpha-platelet. In the case of quasi-smooth facet the alpha-platelet is broken
19
(quasi-brittle fracture) along its elongation direction, figure 4c; in the case of the smooth facet,
20
an individual alpha-platelet is broken by its cross section plane (figure 4). Moreover, the
21
mechanisms of cracking is also different that can be clearly seen based on the analysis of the
22
fracture surface morphologies around these facets. In the case of quasi-smooth facets around
23
these facets a ductile fracture is observed with typical dimples and spherical particles while in
24
the case of smooth facet the surrounded pattern shows a quasi brittle fracture. Both features are
25
associated with a failure of individual alpha-platelet. The analysis of the chemical composition
26
was performed by EDX module integrated into SEM. The chemical composition was studied
7
1
within the crack initiation area: (1) from quasi-smooth facet where the following concentration
2
of beta-stabilizing elements Mo and Cr were detected: molybdenum was 0.65 % weight,
3
chromium was not detected, Al was 8.72 % weight; (2) from smooth facet: concentration of
4
molybdenum was 0.59 % weight, chromium was not detected and aluminum was 7.1 % w. It can
5
be outlined that in the two cases the tendency is the same. There is a very low local concentration
6
of Mo compared with the chemical composition of the VT3-1 alloy (Table 1) in which Mo
7
content is between 2 and 3 % weight.
8
Concluding the results of the fracture surfaces observations the following 'fatigue life
9
controlling' mechanisms of subsurface crack initiation are: initiation from (1) strong defects; (2)
10
border of macro-zones; (3) quasi-smooth facets and (4) smooth facets. According to these
11
mechanisms a multi-modal interpretation of the SN-curve can be proposed, figure 5. According
12
to this interpretation, we assume that a stress-strain incompatibility between ‘matrix’ and critical
13
defect leads to premature failure. In the absence of critical defects on the plane of maximum
14
stress the border of ‘macro-zones’ become a dominating crack initiation mechanism. However,
15
the ‘macro-zone’ is characterized by its size and main crystallographic orientation. So, it means
16
that not all the border has the same potential to block and accumulate dislocations. The crack is
17
initiated from the border of two ‘macro-zones’ with unfavorable mutual orientation. In the case
18
of absence of such adverse orientation, internal crack initiates from smaller features of the
19
microstructure after longer fatigue life.
20
Tensile asymmetric (R=0.1) tests
21
The results of the tests on forged VT3-1 titanium alloy with superimposed static stress
22
(R=0.1) are illustrated in figure 6 (a). The character of fatigue strength decreasing (with the
23
fatigue life) is similar to fully-reversed data and to the results of [19]. However, continuous
24
decreasing of the fatigue strength versus the number of cycles is not always observed in the two-
25
phase titanium alloy. For example in [22] it was reported about clear step of SN - curve for
26
positive stress ratios. We also observed the same thing on the VT3-1 alloy. The results of tensile
8
1
fatigue tests show a higher resistance of VT3-1 under R=0.1 cyclic loads in terms of maximum
2
stress. The fatigue strength of VT3-1 under fully-reversed loading is about 50 MPa lower
3
compared to R=0.1. However, representation of tensile fatigue results in Haigh diagram shows
4
that the resistance of the forged VT3-1 titanium alloy against cyclic loading with imposed static
5
stress is extremely low, figure 6 (b). The results of fatigue tests under R=0.1 are well below
6
Gerber and Goodman predictions of fatigue strength. Such fatigue behavior of VT3-1 titanium
7
alloy can be explained by using the idea of Oguma and Nakamura [22]. They have performed
8
VHCF tests on Ti-6Al-4V titanium alloy under positive stress ratio R=0.1. Titanium alloy was
9
processed by two different treatments producing dual-phase microstructure with alpha-grains
10
sizes of 4 and 10 micrometers respectively. Oguma and Nakamura have found that the alloy with
11
the bigger alpha-grains has the lower fatigue strength. The difference in fatigue strength at 108
12
cycles between Ti-alloys with different grain sizes was 180 MPa. They explain such fatigue
13
behavior by larger ‘effective slip length’ in the material with the bigger grains. ‘Macro-zones’ of
14
forged VT3-1 do also provide a large ‘effective slip length’ for dislocation motion that could
15
lead to important drop of the fatigue strength. It means that the forged VT3-1 has a high
16
sensitivity to static tensile stress in VHCF.
17
Under tensile (R=0.1) the analysis of the fracture surfaces has shown that all the
18
specimens failed because of subsurface crack initiation. All the specimens have crack initiation
19
from the border of ‘macro-zones’, figure 7 (a). It means that in the presence of static tensile
20
stress initiation from the border of macro-zones becomes dominant. Further crack growth is also
21
affected by ‘macro-zones’.
22
The fracture pattern shows large zones (up to several hundred micrometers) of quasi-
23
brittle fracture, figure 7 (b), that is formed due to crack propagation by macro-zones. Probably
24
quasi-brittle fracture is formed due to crack propagation by the border of ‘macro-zones’. Some
25
evidences of that can be observed on the fracture surface as small elements of neighboring
26
structures in figure 7 (c). Several “island-like” typical structures with different orientation of
9
1
alpha-platelets within them were observed. The SEM analysis of these typical structures using
2
back scattering mode has shown that the orientation of the alpha-platelets in these ‘island-like’
3
elements have a difference in the orientation of quasi-brittle fracture pattern, figure 7 (d).
4
Consequently, it seems that the crack propagates near or by the border of large macro-zones
5
(agglomeration of alpha-platelets). Concluding results of SEM observation, it can be outlined
6
that the extremely low resistance to cyclic loading of forged VT3-1 in VHCF regime in the
7
presence of static tensile stress is due to large ‘macro-zones’. These elements become critical
8
under R=0.1 tensile loading and leads to a significant drop of the VHCF strength.
9 10
Torsion fully-reversed (R=-1) tests
11
The results of ultrasonic torsion tests on forged VT3-1 alloy are presented on figure 8 (a).
12
These results show a fatigue strength decreasing with increasing number of loading cycles.
13
Comparing the results of tensile and torsion ultrasonic tests it can be outlined that the slop of the
14
torsion SN-curve is more pronounced. That can be clearly shown by using Von-Mises equivalent
15
stress, figure 8 (b).
16
The results of the fully reversed tensile and torsion tests presented in term of Von-Mises
17
equivalent stress amplitude are close together and grouped around a fatigue strength of 400 MPa.
18
The fatigue life range of specimens failed under torsion is being from (106 to 108 cycles). In the
19
case of tensile loading subsurface crack initiation is mainly due to ‘macro-zones’. Under torsion
20
loading the specimens with the shortest fatigue life show surface crack initiation that is similar to
21
high-cycle fatigue (HCF) regime. However, with decreasing stress amplitude the crack initiation
22
site is shifted to the bulk of the material. It has been found that specimens failed beyond 108
23
cycles exhibit subsurface crack initiation.
24
Subsurface crack initiation is located at a distance of about 200 micrometers from the
25
specimen surface, figure 9 (a). The subsurface crack appears in the plane of maximum shear
26
stress (perpendicular to the specimen’s longitudinal axis). Fracture surface near the crack
10
1
initiation area is significantly destroyed by friction due to contact between crack lips, figure 9
2
(b). Therefore, it is impossible to identify a micro-structural feature that is responsible for crack
3
initiation. Nevertheless, the fracture surface does not show clear crack growth by the border of
4
macro-zones of large zones of quasi-brittle fracture that were observed under tensile loading.
5
When crack becomes longer it bifurcates for propagating on the plane of maximum normal stress
6
(inclined by 45 degrees with respect to the specimen’s axis). The analysis of the crack path at the
7
specimen surface shows that the torsion crack growths on the plane of maximum normal stress
8
up to the final length, figure 9 (c). During this growth, crack may bifurcate to propagate on the
9
maximum shear stress plane (perpendicular or parallel to the specimen axis) but macroscopically
10
the main crack is on the maximum normal stress plane. Some secondary cracks that are in
11
competition with the main crack can be observed at the specimen surface, figure 9 (d). Probably
12
these cracks appear due to the complex microstructure of forged VT3-1.
13
Like under tensile (R=-1) loading the crack path under torsion (R=-1) is influenced by the
14
micro-structure. The crack propagates on different levels by forming complex morphology of the
15
fracture pattern. Sometimes torsion crack meets some microstructural elements that were ‘walk
16
round’ by the crack. Such elements are forcing the crack to propagate on two different planes. It
17
seems that these microstructural elements lead to crack branching that was observed at the
18
specimen surface. But the morphology of the torsion fracture pattern is very perturbed by lips
19
friction that make difficult to distinguish the different stages of crack growth.
20 21
Conclusion
22
Based on ultrasonic fatigue results on aeronautical forged VT3-1 titanium alloy in VHCF
23
regime under different loading modes (tensile and torsion) and stress ratios (R=-1 and R=0.1) the
24
following conclusions can be proposed:
25
1.
26
There are no horizontal asymptotes of the SN-curves for forged VT3-1 under all the tested loading conditions (i.e. no fatigue limits).
11
1
2.
2 3
The slope of the SN - curve is higher for ultrasonic torsion loading compared to the tensile one.
3.
Both surface and subsurface crack initiation were observed under ultrasonic fatigue
4
testing whatever the load type (tension or torsion). In the case of torsion loading the
5
subsurface crack initiation appears in spite of maximum shear stress located at on the
6
specimen surface.
7
4.
In the case of subsurface crack initiation under fully-reversed tensile loading (R=-1) a
8
multi-modal distribution of fatigue life can be proposed. The following fatigue life
9
controlling mechanisms can be outlined: initiation from (a) agglomeration of rough
10
alpha-platelets (strong defect of micro-structure); (b) border of macro-zones; (c) quasi-
11
brittle facets and (d) smooth facet.
12
5.
13 14
In the presence of tensile mean stress the crack initiation mechanism related to macrozones becomes a dominant mechanism.
6.
The torsion crack initiation mechanism was not clearly identified for subsurface crack
15
initiation. However a role of structural elements is important in torsion crack propagation.
16
These elements lead to high crack deviation and branching.
17 18 19
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extruded titanium alloys, FFEMS, Vol.38, Issue 11, p. 1294 – 1304, DOI:
2
10.1111/ffe.12340
3
[15]
Mayer H, Schuller R, Karr U, Irrasch D, Fitzka M, Hahn M, Bacher-Höchst M. (2015),
4
Cyclic torsion very high cycle fatigue of VDSiCr spring steel at different load ratios. Int.
5
J. of Fatigue. 2015: 70; 322–327.
6
[16]
7 8
Issue 7, p. 559–565, DOI: 10.1046/j.1460-2695.1999.00183.x [17]
9 10
C.Bathias, (1999), There is no infinite fatigue life in metallic materials, FFEMS Vol. 22,
C. Bathias, (2013), Fatigue Limit in Metals, Wiley, 128 p., Wiley-ISTE ISBN: 978-184821-476-7
[18]
M. Janecek, F. Novy, P. Harcuba, J.Strasky, L. Trsko, M. Mhaede, L. Wagner, (2015)
11
The very high cycle behaviour of Ti-6Al-4V alloy, Acta Physica Polonica A, Vol.128,
12
pp.497 – 502
13
[19]
J.M. Larsen, S.K. Jha, C.J. Szczepanski, M.J. Caton, R. John, A.H.Rosenberger, D.J.
14
Buchanan, (2013), Reducing uncertainty in fatigue life limits of turbine engine alloys,
15
International Journal of Fatigue, Vol.57, pp. 103 – 112.
16
[20]
A.J. McEvily, T. Nakamura, H. Oguma, K. Yamashita, H. Matsunaga, M. Endo, (2008),
17
On the mechanism of very high cycle fatigue in Ti-6Al-4V, Scripta Materialia, Vol. 59,
18
pp. 1207 – 1209.
19
[21]
M.R. Bache, (2003), A review of dwell sensitive fatigue in titanium alloys: the role of
20
microstructure, texture and operating conditions, International Journal of Fatigue, Vol.
21
25, pp. 1079 – 1087
22 23
[22]
H. Oguma, T. Nakamura, (2010), The effect of microstructure on very high cycle fatigue properties in Ti-6Al-4V, Scripta Materialia, Vol.63, pp. 32-34
24 25 26
14
1
Figures caption
2
Figure 1. Compressor disk of D30 turbojet engine (a), location of specimens in the disk (b), (c)
3
and (d) geometries of tensile specimens, (e) geometry of torsion specimen, (all the dimensions
4
are in mm).
5
Figure 2. Microstructure of forged VT3-1 titanum alloy (a) with typical alpha-platelets (b) that
6
can form agglomerations of different shapes (c) and macro-zones clearly visible by EBSD (d)
7
Figure 3. The SN-curve for forged VT3-1 titanium alloy under fully-reversed (R=-1) tensile
8
fatigue loading at 20 kHz
9
Figure 4. Crack initiations in forged VT3-1 titanium alloy from (a) strong defect, (b) border of
10
macro-zones, (c) quasi-smooth facet and (d) smooth facet
11
Figure 5 Multi-modal SN-curve for forged VT3-1 under fully-reversed (R=-1) tensile loading at
12
20 kHz
13
Figure 6 (a) SN-curve for forged VT3-1 under asymmetric (R=0.1) tensile loading and (b) Haigh
14
diagram with Goodman and Gerber threshold.
15
Figure 7 Subsurface crack morphology in forged VT3-1 titanium alloy under R=0.1 tensile
16
loading (a) crack initiation from the border of macro-zone, (b) crack growth within macro-zones,
17
(c) ‘island-like’ typical structure on the fracture pattern and (d) back scatter electrons image of
18
‘island-like’ structure.
19
Figure 8 SN-curve of the forged VT3-1 alloy under: (a) torsion (R=-1) in terms of shear stress
20
amplitude and (b) tensile (R=-1) and torsion (R=-1) results in terms of Von-Mises equivalent
21
stress amplitude.
22
Figure 9. Torsion crack in forged VT3-1 titanium alloy (a) overview on fracture pattern, (b)
23
crack initiation site, (c) crack path at specimen surface and (d) branching of torsion crack on
24
specimen surface.
25
15
1 2 3 4 5 6
Highlights Very High Cycle Fatigue regime for titanium alloy VT3-1. Material state for specimens manufactured from titanium disk. Subsurface crack origination on specimens under tension and torsion loads. Fracture surface features for different stress ratios.
16
Figure
List of figures
Figure 1. Compressor disk of D30 turbojet engine (a), location of specimens in the disk (b), (c) and (d) geometries of tensile specimens, (e) geometry of torsion specimens, all the dimensions are in mm.
Figure 2. Microstructure of forged VT3-1 titanum alloy (a) with typical alpha-platelets (b) that can form agglomerations of different shapes (c) and macro-zones clearly visible by EBSD (d)
Figure 3. The SN-curve for forged VT3-1 titanium alloy under fully-reversed (R=-1) tensile fatigue loading at 20 kHz
Figure 4. Crack initiations in forged VT3-1 titanium alloy from (a) strong defect, (b) border of macro-zones, (c) quasi-smooth facet and (d) smooth facet
Figure 5 Multi-modal SN-curve for forged VT3-1 under fully-reversed (R=-1) tensile loading at 20 kHz
Figure 6 (a) SN-curve for forged VT3-1 under asymmetric (R=0.1) tensile loading and (b) Haigh diagram with Goodman and Gerber threshold.
Figure 7 Subsurface crack morphology in forged VT3-1 titanium alloy under R=0.1 tensile loading (a) crack initiation from the border of macro-zone, (b) crack growth within macro-zones, (c) ‘island-like’ typical structure on the fracture pattern and (d) back scatter electrons image of ‘island-like’ structure.
Figure 8 SN-curve of forged VT3-1 alloy under (a) torsion (R=-1) in terms of shear stress amplitude and (b) tensile (R=-1) and torsion (R=-1) results in terms of Von-Mises equivalent stress amplitude
Figure 9. Torsion crack in forged VT3-1 titanium alloy (a) overview on fracture pattern, (b) crack initiation site, (c) crack path at specimen surface and (d) branching of torsion crack on specimen surface.
S0142-1123(16)30138-4 http://dx.doi.org/10.1016/j.ijfatigue.2016.05.030 JIJF 3979
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
15 February 2016 24 May 2016 26 May 2016
Please cite this article as: Nikitin, A., Palin-Luc, T., Shanyavskiy, A., Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes, International Journal of Fatigue (2016), doi: http:// dx.doi.org/10.1016/j.ijfatigue.2016.05.030
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1
Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion
2
loading modes
3
A. Nikitin1,2, T. Palin-Luc 3, A. Shanyavskiy 2, 4*
4
1
5
France
6
2
7
Russia
8
3
9
Metiers, Talence, 33405, France
10
4
LEME, University Paris Ouest Nanterre La Defense, 50, rue de Serves, Ville-d'Avray, 92410,
MAI – National Research University, 4, Volokolamskoe Hwy, A-80, GSP-3, Moscow, 125993,
Arts et Metiers Paris Tech, I2M, CNRS, Universite de Bordeaux, Esplanade des Arts et
SCCAFS, Air. Sheremetevo-1, PO Box 54, Moscow reg., Chimkovskiy state, 141426, Russia
11 12
emails : [email protected], [email protected], [email protected]
13 14
Abstract. This paper is focused on the VHCF behavior of aeronautical titanium alloy
15
under tensile and torsion fatigue loading. Tensile tests were carried out with two different stress
16
ratios: R=-1 and R=0.1. Both surface and subsurface crack initiations were observed. In the case
17
of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were
18
found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-
19
zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R=0.1, have
20
shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation
21
mechanism in presence of positive mean stress. Like for the tensile results, surface and
22
subsurface crack initiation were observed under ultrasonic torsion in spite of the maximum shear
23
stress location on the specimen surface. But the real reason for the subsurface crack initiation
24
under torsion was not found.
25
Keywords: Very-high cycle fatigue, titanium alloy, crack initiation, ultrasonic torsion
26
1
1
Introduction. The problem of fatigue in aeronautical application has a long history [1, 2]
2
and for a long time it was assumed (considered) as low (LCF) and high cycle fatigue (HCF)
3
problems. These two domains were deeply studied for different aeronautical materials, such as
4
aluminum, titanium and nickel based alloys [3]. However, in spite of the developed knowledge
5
about the fatigue behavior of aeronautical materials in the LCF and HCF regimes, some
6
‘unexpected’ in-service failures were reported [4, 5, 6] for compressor and turbine. One of the
7
most critical elements of the aircraft in terms of ‘unexpected failure’ is the turbojet engine. The
8
analysis of typical loading spectrum for blades of turbojet engine has shown that the number of
9
loading cycles for such application can reach 10 10 cycles during in service [7]. The regime of
10
fatigue with ultra long fatigue life is known as very high cycle fatigue (VHCF) or Gigacycle
11
fatigue. Convenient experimental methods are purposed to estimate the fatigue strength at much
12
lower fatigue life (about 10 7, maximum 108 cycles) that is 2 -3 orders of magnitude shorter
13
compared to the real life. Consequentially, conclusion of Nicholas [4] about a premature in-
14
service fatigue failure of titanium compressor of military aircraft was the following: ‘unexpected
15
fatigue failure was due to high frequency loading that lead to accumulation about 10 9 loading
16
cycles during in-service’. Moreover, the fatigue behavior of material in VHCF regime is very
17
sensitive to microstructural features of materials that lead to different types of SN-curves [8].
18
Therefore, nowadays it is impossible to determine the parameters of the SN-curve of a material
19
in VHCF regime without experiment.
20
Usually the critical stress-strain state of fatigue on real elements is estimated by using
21
multiaxial criteria. However, there are no ultrasonic testing methods for multi-axial loading. The
22
only solution for developing multiaxial criteria in VHCF regime is using several testing systems
23
for different loading conditions. Bathias has developed numerous of ultrasonic testing machines
24
such as tension-compression, tension-tension, three points bending [9], torsion [10] and some
25
other systems [7, 11]. It has been shown that the crack initiation mechanism under different
26
loading conditions can be different.
2
1
The purpose of this work is to investigate the crack initiation mechanisms in aeronautical
2
VT3-1 titanium alloy under different loading conditions. Tensile tests under different load ratios
3
were performed together with ultrasonic torsion. Fracture surfaces of all the tested specimens
4
were investigated by SEM in order to identify the crack initiation mechanism.
5 Material and experimental procedure
6
Material
7 8
The studied material in the present work is the forged VT3-1 titanium alloy that is
9
commonly used in the aeronautic industry for compressor disks and blades production. All the
10
specimens were machined from a real compressor disk of a D30 turbojet engine used for Tu-154
11
aircraft, figure 1a.
12
The disk has flown about 16,000 hours. The in-service flown disk was submitted to non
13
destructive controls (ultrasonic NDT and alternating current field measurement) in order to
14
estimate possible accumulated in-service fatigue damages. The results of this after service
15
controls did not reveal degradation of the material due to fatigue (no cracks or material defects).
16
The chemical composition of forged titanium alloy respects to the State standards [12], (Table
17
1).
18 19
Table 1. Chemical composition of forged VT3-1 titanium alloy (w, %) Fe
C
Si
Cr
Mo
N
Al
Zr
O
H
0.2 - 0.7
< 0.1
0.15 - 0.4
0.8 - 2
2-3
< 0.05
5.5 - 7
< 0.5
< 0.15
< 0.015
20 21
The microstructure of this forged VT3-1 titanium alloy is shown in figure 2a. One can see
22
by elongated alpha-platelets with typical length of 10 – 15 micrometers and width of 2-3
23
micrometers, figure 2b. Macroscopically the microstructure of this titanium alloy is strongly
24
inhomogeneous with clear alpha-platelets agglomerations of different sizes and shapes, figure 2c.
3
1
Besides local agglomerations the microstructure is also represented by large continuous areas
2
that are filled with thin, similarly orientated alpha-platelets, figure 2d. Such areas were already
3
observed in a forged titanium alloy and reported in the literature as 'macro-zones' [13].
4
The micro-hardness of this titanium alloy is also inhomogeneous that is stated based on
5
measurements along the specimen’s cross-section diameter. The average value of micro-hardness
6
is 364 HV500 with a maximum deviation of 44 HV500. The value of micro-hardness is related
7
to geometry of alpha-platelets at the location of measurement. Where there is an agglomeration
8
of rough alpha-platelets the micro-hardness value is higher compared to the areas with finer
9
platelets (398 HV for rough and 238 HV for fine alpha-platelets).
10
The mechanical properties were studied by using small tensile specimens machined from
11
the disk’s web, figure 1. Blanks for tensile specimen were taken in circumferential direction. Flat
12
tensile specimens had a thickness of 1 mm, a total length of 75 mm, a length of the working
13
section of 25 mm and a working section width of 5 mm. Monotonic tensile tests were carried out
14
with a displacement rate of 0,075 mm/min. Additionally, the dynamic modulus was determined
15
at 20 kHz. All the mechanical properties are given in Table 2.
16 17
Table 2. Mechanical properties of forged VT3-1 titanium alloy Young's modulus,
UTS [MPa]
[GPa] 114
989
Yield
Elongation
Volumetric
Dynamic
stress
at rupture
mass
modulus
[MPa]
[%]
kg.m-3
[GPa]
960
6
4500
116
18 19
Experimental procedures
20
Two types of fatigue tests in VHCF regime (tensile and torsion) were carried out by using
21
ultrasonic fatigue testing systems. Tensile fatigue tests were performed on a LASUR
22
piezoelectric machine [7] under fully reversed (R=-1) and asymmetric (R=0.1) loadings at 20
4
1
kHz up to the specimen failure or run-out limit of 5x109 cycles for the tensile tests and 109 cycles
2
for the torsion one. The torsion fatigue tests were performed on a self-designed piezoelectric
3
torsion system [14] under fully-reversed (R=-1) loading. All the tests were carried out in
4
laboratory air at room temperature (compressed air cooling). The temperature of the specimen
5
surface was measured by infrared camera measurements for some of the tested specimens. To do
6
that, some tensile and torsion specimens were painted in matt black for the tests with surface
7
temperature measurement at different stress levels (from 100 to 400 MPa for tensile tests and
8
240 MPa for torsion). All the tests were performed with air cooling (like under all the fatigue
9
tests) and a base for one test was 5 ⋅ 10 6 cycles. It was pointed out that at each load level the
10
surface temperature gets stable (horizontal line on graph temperature versus time) after a few
11
seconds of the test. The results of these tests have shown that the maximum increase of
12
temperature due to self heating was less than 10 oC [14].
13
Specimens for ultrasonic fatigue tests were machined from different areas of the
14
compressor disk, figure 1b. Tensile fatigue specimens, figure 1c and 1d were machined from
15
both the rim and the web parts of the disk while torsion specimens, figure 1e, were cut from the
16
rim part only. Several sets of tensile fatigue specimens were prepared: (1) specimens for fully-
17
reversed (R=-1) tests were machined from the rim part in axial direction, figure 1b and from web
18
part in radial direction; (2) specimens for asymmetric (R=0.1) tests were machined from web
19
part in radial and circumferential directions, figure 1b. The surface of all the specimens was
20
mechanically polished with emery paper up to grade 1000. Machining and mechanical polishing
21
may introduce a residual stresses that could affect the crack initiation mechanism. These residual
22
stresses could lead to near to surface crack initiation. Such influence of residual stresses was
23
already discussed for the case of ultrasonic torsion tests on steels. It was found that subsurface
24
torsion crack can initiate from the subsurface in the presence of high residual stresses [15]. In the
25
present study the residual stresses were not measured due to limitations of X-ray diffraction
5
1
instrument because of the complex microstructure of this alloy. The uncertainty of the
2
measurements was higher that the measured values.
3 4
Results and discussions Tensile fully-reversed (R=-1) tests
5
The results of the tests are presented in figure 3. As usual with increasing stress
6
amplitude the fatigue life decreases but we can observe very large scatter. In HCF regime fatigue
7
failures were mainly observed under stress amplitudes of 415 – 430 MPa that is about 43% of
8
ultimate tensile strength. However, there is one stand out result that was obtained under lower
9
stress amplitude after a short fatigue life (in HCF region). The fracture surface analysis by SEM
10
for this specimen has shown subsurface crack initiation with quite damaged origination site. It
11
seems that such initiation is related to some sort of microstructural defect that was not yet found
12
on observed micro-sections. The results of the fatigue tests show a large scatter of fatigue life
13
that reach three orders of magnitude under certain stress amplitudes. In spite of so large scatter a
14
trend line built by least square method is straight decreasing line with clear slope of the SN -
15
curve. Thus, we can say that forged VT3-1 does not show a horizontal asymptote like many
16
others structural materials [8] and there is no infinite fatigue life [16, 17]. A similar result has
17
been reported for Ti-6Al-4V titanium alloy by Janecek [18] in VHCF regime under fully-
18
reversed loading (R=-1) at 20 kHz. It has been stated that the SN curves exhibit a continuous
19
decrease of the stress amplitude with increasing number of cycles from 104 to 109 cycles.
20
In our experiments the analysis of the fracture surfaces has shown two principal crack
21
initiation locations: surface and subsurface. This result is common for two-phase titanium alloy
22
and was already reported for different alloy [18, 19]. However, in order to understand the reason
23
of so large scatter of the fatigue life (figure 3), the fracture surface of all the specimens was
24
analyzed by using scanning electron microscope (SEM). From these fractographic analyses it
25
was found that under high stress amplitudes and short fatigue life crack initiation site is observed
26
at the specimen surface. Detailed analysis on crack initiation sites by SEM allows us to outline
6
1
several 'fatigue life controlling' mechanisms. Specimens with shorter fatigue life and subsurface
2
crack initiations have a strong defect of the microstructure at crack initiation site, figure 4a.
3
Strong defects of microstructure produce a quasi-brittle pattern with clear traces of cracked
4
alpha-platelets. The geometry of these quasi-brittle zones and traces of alpha-platelet allow us to
5
associate these defects with an agglomeration of rough alpha-platelets, figure 2c.
6
With increasing the fatigue life there is a quota of specimens with crack initiation from
7
strong defects is decreasing. In this case another crack initiation mechanism starts to dominate
8
over the previous one. In longer fatigue life, fatigue crack is typically initiated from the border of
9
‘macro-zones’ that are large areas formed by similarly orientated alpha-platelets [13], figure 4b.
10
Within such zone all the alpha-platelets have almost the same crystallographic orientation that
11
allows easier dislocation moving on long distance. The border of two 'macro-zones' is an
12
important barrier for dislocation moving that makes the 'macro-zone' border a stock of the large
13
number of dislocations. Micro-plasticity accumulated at 'macro-zones' borders lead to crack
14
initiation.
15
The specimens failed after longest fatigue lives are typically showing two similar crack
16
initiation sites: quasi-smooth and smooth facets, figure 4c and 4d respectively. These facets are
17
formed due to failure of alpha-platelets or alpha-grains [20, 21]. Figure 4 c and d illustrate a 3D
18
model of individual alpha-platelet. In the case of quasi-smooth facet the alpha-platelet is broken
19
(quasi-brittle fracture) along its elongation direction, figure 4c; in the case of the smooth facet,
20
an individual alpha-platelet is broken by its cross section plane (figure 4). Moreover, the
21
mechanisms of cracking is also different that can be clearly seen based on the analysis of the
22
fracture surface morphologies around these facets. In the case of quasi-smooth facets around
23
these facets a ductile fracture is observed with typical dimples and spherical particles while in
24
the case of smooth facet the surrounded pattern shows a quasi brittle fracture. Both features are
25
associated with a failure of individual alpha-platelet. The analysis of the chemical composition
26
was performed by EDX module integrated into SEM. The chemical composition was studied
7
1
within the crack initiation area: (1) from quasi-smooth facet where the following concentration
2
of beta-stabilizing elements Mo and Cr were detected: molybdenum was 0.65 % weight,
3
chromium was not detected, Al was 8.72 % weight; (2) from smooth facet: concentration of
4
molybdenum was 0.59 % weight, chromium was not detected and aluminum was 7.1 % w. It can
5
be outlined that in the two cases the tendency is the same. There is a very low local concentration
6
of Mo compared with the chemical composition of the VT3-1 alloy (Table 1) in which Mo
7
content is between 2 and 3 % weight.
8
Concluding the results of the fracture surfaces observations the following 'fatigue life
9
controlling' mechanisms of subsurface crack initiation are: initiation from (1) strong defects; (2)
10
border of macro-zones; (3) quasi-smooth facets and (4) smooth facets. According to these
11
mechanisms a multi-modal interpretation of the SN-curve can be proposed, figure 5. According
12
to this interpretation, we assume that a stress-strain incompatibility between ‘matrix’ and critical
13
defect leads to premature failure. In the absence of critical defects on the plane of maximum
14
stress the border of ‘macro-zones’ become a dominating crack initiation mechanism. However,
15
the ‘macro-zone’ is characterized by its size and main crystallographic orientation. So, it means
16
that not all the border has the same potential to block and accumulate dislocations. The crack is
17
initiated from the border of two ‘macro-zones’ with unfavorable mutual orientation. In the case
18
of absence of such adverse orientation, internal crack initiates from smaller features of the
19
microstructure after longer fatigue life.
20
Tensile asymmetric (R=0.1) tests
21
The results of the tests on forged VT3-1 titanium alloy with superimposed static stress
22
(R=0.1) are illustrated in figure 6 (a). The character of fatigue strength decreasing (with the
23
fatigue life) is similar to fully-reversed data and to the results of [19]. However, continuous
24
decreasing of the fatigue strength versus the number of cycles is not always observed in the two-
25
phase titanium alloy. For example in [22] it was reported about clear step of SN - curve for
26
positive stress ratios. We also observed the same thing on the VT3-1 alloy. The results of tensile
8
1
fatigue tests show a higher resistance of VT3-1 under R=0.1 cyclic loads in terms of maximum
2
stress. The fatigue strength of VT3-1 under fully-reversed loading is about 50 MPa lower
3
compared to R=0.1. However, representation of tensile fatigue results in Haigh diagram shows
4
that the resistance of the forged VT3-1 titanium alloy against cyclic loading with imposed static
5
stress is extremely low, figure 6 (b). The results of fatigue tests under R=0.1 are well below
6
Gerber and Goodman predictions of fatigue strength. Such fatigue behavior of VT3-1 titanium
7
alloy can be explained by using the idea of Oguma and Nakamura [22]. They have performed
8
VHCF tests on Ti-6Al-4V titanium alloy under positive stress ratio R=0.1. Titanium alloy was
9
processed by two different treatments producing dual-phase microstructure with alpha-grains
10
sizes of 4 and 10 micrometers respectively. Oguma and Nakamura have found that the alloy with
11
the bigger alpha-grains has the lower fatigue strength. The difference in fatigue strength at 108
12
cycles between Ti-alloys with different grain sizes was 180 MPa. They explain such fatigue
13
behavior by larger ‘effective slip length’ in the material with the bigger grains. ‘Macro-zones’ of
14
forged VT3-1 do also provide a large ‘effective slip length’ for dislocation motion that could
15
lead to important drop of the fatigue strength. It means that the forged VT3-1 has a high
16
sensitivity to static tensile stress in VHCF.
17
Under tensile (R=0.1) the analysis of the fracture surfaces has shown that all the
18
specimens failed because of subsurface crack initiation. All the specimens have crack initiation
19
from the border of ‘macro-zones’, figure 7 (a). It means that in the presence of static tensile
20
stress initiation from the border of macro-zones becomes dominant. Further crack growth is also
21
affected by ‘macro-zones’.
22
The fracture pattern shows large zones (up to several hundred micrometers) of quasi-
23
brittle fracture, figure 7 (b), that is formed due to crack propagation by macro-zones. Probably
24
quasi-brittle fracture is formed due to crack propagation by the border of ‘macro-zones’. Some
25
evidences of that can be observed on the fracture surface as small elements of neighboring
26
structures in figure 7 (c). Several “island-like” typical structures with different orientation of
9
1
alpha-platelets within them were observed. The SEM analysis of these typical structures using
2
back scattering mode has shown that the orientation of the alpha-platelets in these ‘island-like’
3
elements have a difference in the orientation of quasi-brittle fracture pattern, figure 7 (d).
4
Consequently, it seems that the crack propagates near or by the border of large macro-zones
5
(agglomeration of alpha-platelets). Concluding results of SEM observation, it can be outlined
6
that the extremely low resistance to cyclic loading of forged VT3-1 in VHCF regime in the
7
presence of static tensile stress is due to large ‘macro-zones’. These elements become critical
8
under R=0.1 tensile loading and leads to a significant drop of the VHCF strength.
9 10
Torsion fully-reversed (R=-1) tests
11
The results of ultrasonic torsion tests on forged VT3-1 alloy are presented on figure 8 (a).
12
These results show a fatigue strength decreasing with increasing number of loading cycles.
13
Comparing the results of tensile and torsion ultrasonic tests it can be outlined that the slop of the
14
torsion SN-curve is more pronounced. That can be clearly shown by using Von-Mises equivalent
15
stress, figure 8 (b).
16
The results of the fully reversed tensile and torsion tests presented in term of Von-Mises
17
equivalent stress amplitude are close together and grouped around a fatigue strength of 400 MPa.
18
The fatigue life range of specimens failed under torsion is being from (106 to 108 cycles). In the
19
case of tensile loading subsurface crack initiation is mainly due to ‘macro-zones’. Under torsion
20
loading the specimens with the shortest fatigue life show surface crack initiation that is similar to
21
high-cycle fatigue (HCF) regime. However, with decreasing stress amplitude the crack initiation
22
site is shifted to the bulk of the material. It has been found that specimens failed beyond 108
23
cycles exhibit subsurface crack initiation.
24
Subsurface crack initiation is located at a distance of about 200 micrometers from the
25
specimen surface, figure 9 (a). The subsurface crack appears in the plane of maximum shear
26
stress (perpendicular to the specimen’s longitudinal axis). Fracture surface near the crack
10
1
initiation area is significantly destroyed by friction due to contact between crack lips, figure 9
2
(b). Therefore, it is impossible to identify a micro-structural feature that is responsible for crack
3
initiation. Nevertheless, the fracture surface does not show clear crack growth by the border of
4
macro-zones of large zones of quasi-brittle fracture that were observed under tensile loading.
5
When crack becomes longer it bifurcates for propagating on the plane of maximum normal stress
6
(inclined by 45 degrees with respect to the specimen’s axis). The analysis of the crack path at the
7
specimen surface shows that the torsion crack growths on the plane of maximum normal stress
8
up to the final length, figure 9 (c). During this growth, crack may bifurcate to propagate on the
9
maximum shear stress plane (perpendicular or parallel to the specimen axis) but macroscopically
10
the main crack is on the maximum normal stress plane. Some secondary cracks that are in
11
competition with the main crack can be observed at the specimen surface, figure 9 (d). Probably
12
these cracks appear due to the complex microstructure of forged VT3-1.
13
Like under tensile (R=-1) loading the crack path under torsion (R=-1) is influenced by the
14
micro-structure. The crack propagates on different levels by forming complex morphology of the
15
fracture pattern. Sometimes torsion crack meets some microstructural elements that were ‘walk
16
round’ by the crack. Such elements are forcing the crack to propagate on two different planes. It
17
seems that these microstructural elements lead to crack branching that was observed at the
18
specimen surface. But the morphology of the torsion fracture pattern is very perturbed by lips
19
friction that make difficult to distinguish the different stages of crack growth.
20 21
Conclusion
22
Based on ultrasonic fatigue results on aeronautical forged VT3-1 titanium alloy in VHCF
23
regime under different loading modes (tensile and torsion) and stress ratios (R=-1 and R=0.1) the
24
following conclusions can be proposed:
25
1.
26
There are no horizontal asymptotes of the SN-curves for forged VT3-1 under all the tested loading conditions (i.e. no fatigue limits).
11
1
2.
2 3
The slope of the SN - curve is higher for ultrasonic torsion loading compared to the tensile one.
3.
Both surface and subsurface crack initiation were observed under ultrasonic fatigue
4
testing whatever the load type (tension or torsion). In the case of torsion loading the
5
subsurface crack initiation appears in spite of maximum shear stress located at on the
6
specimen surface.
7
4.
In the case of subsurface crack initiation under fully-reversed tensile loading (R=-1) a
8
multi-modal distribution of fatigue life can be proposed. The following fatigue life
9
controlling mechanisms can be outlined: initiation from (a) agglomeration of rough
10
alpha-platelets (strong defect of micro-structure); (b) border of macro-zones; (c) quasi-
11
brittle facets and (d) smooth facet.
12
5.
13 14
In the presence of tensile mean stress the crack initiation mechanism related to macrozones becomes a dominant mechanism.
6.
The torsion crack initiation mechanism was not clearly identified for subsurface crack
15
initiation. However a role of structural elements is important in torsion crack propagation.
16
These elements lead to high crack deviation and branching.
17 18 19
References
[1]
20 21
W. Schutz, (1996), A history of fatigue, Engineering Fracture Mechanics, Vol.54, Issue 2, p. 263 – 300, DOI: 10.1016/0013-7944(95)00178-6
[2]
M.R. Bache, W.J. Evans, (1992), Tension and torsion fatigue testing of a near-alpha
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titanium alloy, Int. J. of Fatigue, Vol.14, Issue 5, p. 331 – 337, doi:10.1016/0142-
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1123(92)90485-U
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[3]
A. Shanyavskiy, (2007), Modeling of fatigue failure in metals. Synergetic in aeronautic, Monographiya, Ufa, 498 p., ISBN: 978-5-94920-058-2
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A. Shanyavskiy, (2014), Very-High-Cycle-Fatigue of in-service air-engine blades, Science China Physics, Mechanics & Astronomy, Vol.57 Issue.1, pp.19-29
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T. Nicolas, (1999), Critical issues in high cycle fatigue, Int. J. of Fatigue, vol. 21, S221 –
C.Bathias, P.C. Paris, (2005), Gigacycle Fatigue in Mechanical Practice, Dekker, NewYork, 328 p., ISBN 9780824723132
[8]
C.Bathias, L. Drouillac, P. Le Francois, (2001), How and why the fatigue S–N curve does
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not approach a horizontal asymptote, Int. J. of Fatigue, Vol. 23, Sup.1, p.143 – 151,
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doi:10.1016/S0142-1123(01)00123-2
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[9]
H.Q.Xue, H. Tao, F. Montembault, Q.Y.Wang, C.Bathias, (2007), Developing of a three-
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point bending fatigue testing methodology at 20 kHz frequency, International Journal of
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Fatigue, Vol. 29, 2085 – 2093, doi:10.1016/j.ijfatigue.2007.03.018
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[10]
E. Bayraktar, H.Xue, F. Ayari, C. Bathias, (2010), Torsion fatigue behaviour and damage
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mechanisms in the very high cycle regime, Archives of Materials Science and
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Engineering, Vol. 43, Issue 2, pp. 77 – 86.
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C. Bathias, (2006), Piezoelectric fatigue testing machines and devices, Int. J. of Fatigue, Vol. 28, Issue 11, pp. 1438 – 1445. DOI: 10.1016/j.ijfatigue.2005.09.020
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[12]
Russian State Standard GOST-19807-91 (2009), Titanium and wrought titanium alloys.
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[13]
K. LeBiavant, S. Pommier and C. Prioul, (2003), Local texture and fatigue crack
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initiation in Ti-6Al-4V titanium alloy, FFEMS, Vol.25, pp. 527 – 545, DOI:
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10.1046/j.1460-2695.2002.00480.x
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[14]
A.Nikitin, C. Bathias and T. Palin-Luc, (2015), A new piezoelectric fatigue testing machine in pure torsion for ultrasonic gigacycle fatigue tests: application to forged and
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1
extruded titanium alloys, FFEMS, Vol.38, Issue 11, p. 1294 – 1304, DOI:
2
10.1111/ffe.12340
3
[15]
Mayer H, Schuller R, Karr U, Irrasch D, Fitzka M, Hahn M, Bacher-Höchst M. (2015),
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Cyclic torsion very high cycle fatigue of VDSiCr spring steel at different load ratios. Int.
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J. of Fatigue. 2015: 70; 322–327.
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Issue 7, p. 559–565, DOI: 10.1046/j.1460-2695.1999.00183.x [17]
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C.Bathias, (1999), There is no infinite fatigue life in metallic materials, FFEMS Vol. 22,
C. Bathias, (2013), Fatigue Limit in Metals, Wiley, 128 p., Wiley-ISTE ISBN: 978-184821-476-7
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M. Janecek, F. Novy, P. Harcuba, J.Strasky, L. Trsko, M. Mhaede, L. Wagner, (2015)
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The very high cycle behaviour of Ti-6Al-4V alloy, Acta Physica Polonica A, Vol.128,
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pp.497 – 502
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J.M. Larsen, S.K. Jha, C.J. Szczepanski, M.J. Caton, R. John, A.H.Rosenberger, D.J.
14
Buchanan, (2013), Reducing uncertainty in fatigue life limits of turbine engine alloys,
15
International Journal of Fatigue, Vol.57, pp. 103 – 112.
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[20]
A.J. McEvily, T. Nakamura, H. Oguma, K. Yamashita, H. Matsunaga, M. Endo, (2008),
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On the mechanism of very high cycle fatigue in Ti-6Al-4V, Scripta Materialia, Vol. 59,
18
pp. 1207 – 1209.
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[21]
M.R. Bache, (2003), A review of dwell sensitive fatigue in titanium alloys: the role of
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microstructure, texture and operating conditions, International Journal of Fatigue, Vol.
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25, pp. 1079 – 1087
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H. Oguma, T. Nakamura, (2010), The effect of microstructure on very high cycle fatigue properties in Ti-6Al-4V, Scripta Materialia, Vol.63, pp. 32-34
24 25 26
14
1
Figures caption
2
Figure 1. Compressor disk of D30 turbojet engine (a), location of specimens in the disk (b), (c)
3
and (d) geometries of tensile specimens, (e) geometry of torsion specimen, (all the dimensions
4
are in mm).
5
Figure 2. Microstructure of forged VT3-1 titanum alloy (a) with typical alpha-platelets (b) that
6
can form agglomerations of different shapes (c) and macro-zones clearly visible by EBSD (d)
7
Figure 3. The SN-curve for forged VT3-1 titanium alloy under fully-reversed (R=-1) tensile
8
fatigue loading at 20 kHz
9
Figure 4. Crack initiations in forged VT3-1 titanium alloy from (a) strong defect, (b) border of
10
macro-zones, (c) quasi-smooth facet and (d) smooth facet
11
Figure 5 Multi-modal SN-curve for forged VT3-1 under fully-reversed (R=-1) tensile loading at
12
20 kHz
13
Figure 6 (a) SN-curve for forged VT3-1 under asymmetric (R=0.1) tensile loading and (b) Haigh
14
diagram with Goodman and Gerber threshold.
15
Figure 7 Subsurface crack morphology in forged VT3-1 titanium alloy under R=0.1 tensile
16
loading (a) crack initiation from the border of macro-zone, (b) crack growth within macro-zones,
17
(c) ‘island-like’ typical structure on the fracture pattern and (d) back scatter electrons image of
18
‘island-like’ structure.
19
Figure 8 SN-curve of the forged VT3-1 alloy under: (a) torsion (R=-1) in terms of shear stress
20
amplitude and (b) tensile (R=-1) and torsion (R=-1) results in terms of Von-Mises equivalent
21
stress amplitude.
22
Figure 9. Torsion crack in forged VT3-1 titanium alloy (a) overview on fracture pattern, (b)
23
crack initiation site, (c) crack path at specimen surface and (d) branching of torsion crack on
24
specimen surface.
25
15
1 2 3 4 5 6
Highlights Very High Cycle Fatigue regime for titanium alloy VT3-1. Material state for specimens manufactured from titanium disk. Subsurface crack origination on specimens under tension and torsion loads. Fracture surface features for different stress ratios.
16
Figure
List of figures
Figure 1. Compressor disk of D30 turbojet engine (a), location of specimens in the disk (b), (c) and (d) geometries of tensile specimens, (e) geometry of torsion specimens, all the dimensions are in mm.
Figure 2. Microstructure of forged VT3-1 titanum alloy (a) with typical alpha-platelets (b) that can form agglomerations of different shapes (c) and macro-zones clearly visible by EBSD (d)
Figure 3. The SN-curve for forged VT3-1 titanium alloy under fully-reversed (R=-1) tensile fatigue loading at 20 kHz
Figure 4. Crack initiations in forged VT3-1 titanium alloy from (a) strong defect, (b) border of macro-zones, (c) quasi-smooth facet and (d) smooth facet
Figure 5 Multi-modal SN-curve for forged VT3-1 under fully-reversed (R=-1) tensile loading at 20 kHz
Figure 6 (a) SN-curve for forged VT3-1 under asymmetric (R=0.1) tensile loading and (b) Haigh diagram with Goodman and Gerber threshold.
Figure 7 Subsurface crack morphology in forged VT3-1 titanium alloy under R=0.1 tensile loading (a) crack initiation from the border of macro-zone, (b) crack growth within macro-zones, (c) ‘island-like’ typical structure on the fracture pattern and (d) back scatter electrons image of ‘island-like’ structure.
Figure 8 SN-curve of forged VT3-1 alloy under (a) torsion (R=-1) in terms of shear stress amplitude and (b) tensile (R=-1) and torsion (R=-1) results in terms of Von-Mises equivalent stress amplitude
Figure 9. Torsion crack in forged VT3-1 titanium alloy (a) overview on fracture pattern, (b) crack initiation site, (c) crack path at specimen surface and (d) branching of torsion crack on specimen surface.